High-Throughput Quantification of Altermagnetic Band Splitting

TL;DR

This work addresses the challenge of discovering altermagnetic materials, a symmetry-protected, zero-net-magnetization phase with momentum-dependent spin polarization that does not require spin–orbit coupling. The authors implement a two-stage high-throughput workflow combining symmetry analysis (amcheck) on MAGNDATA with spin-polarized DFT (VASP) to identify and characterize altermagnetic candidates, reporting 171 robust materials with spin splitting greater than 50 meV within ±3 eV of the Fermi level. The results reveal momentum-resolved, symmetry-driven spin splitting that varies across the Brillouin zone and is often maximal away from high-symmetry paths, informing future ARPES experiments. An open-access database accompanies the study, providing a scalable blueprint for discovering altermagnetic and related spintronic materials.

Abstract

Altermagnetism represents a recently established class of collinear magnetism that combines zero net magnetization with momentum-dependent spin polarization, enabled by symmetry constraints rather than spin-orbit coupling. This distinctive behavior gives rise to sizable spin splitting even in materials composed of light, earth-abundant elements, offering promising prospects for next-generation spintronics applications. Despite growing theoretical and experimental interest, the discovery of altermagnetic materials remains limited due to the complexity of magnetic symmetry and the inefficiency of conventional approaches. Here, we present a comprehensive high-throughput screening of the entire MAGNDATA database, integrating symmetry analysis with spin-polarized density functional theory (DFT) calculations to identify and characterize altermagnetic candidates. Our workflow uncovers 173 materials exhibiting significant spin splitting ($\geq 50$ meV within $\pm 3$ eV of the Fermi level), spanning both metallic and semiconducting systems. Crucially, our momentum-resolved analysis reveals that the spin splitting varies strongly across the Brillouin zone, and that the maximal splitting tends to occur away from the high-symmetry paths, a result that directly informs and guides future photoemission experiments. By expanding the catalog of known altermagnets and elucidating the symmetry-protected origins of spin splitting, this work lays a robust foundation for future experimental and theoretical advances in spintronics and quantum materials discovery.

Figures (4)

• Figure 1: Two-stage high-throughput computational workflow to identify candidate altermagnetic materials (AMs).(a) Initial screening selects experimentally characterized magnetic materials from the MAGNDATA database. Symmetry analysis via amcheck followed by deduplication filtering step, yielding a final set of 188 unique AM candidates. (b) In-depth computational verification using spin-polarized DFT calculations (VASP, pymatgen, and httk). Materials exhibiting spin splitting ($\ge$50 meV within $\pm$3 eV of $E_F$) are confirmed as AM and included in the final database.
• Figure 2: Structural, electronic, and spin-resolved properties of UCr$_2$Si$_2$C.(a) Side view of the crystal structure of UCr$_2$Si$_2$C, illustrating the magnetic configuration with arrows representing spin orientations. (b) Corresponding Brillouin zone (BZ) indicating key high-symmetry points. (c) Spin-polarized electronic band structure along high-symmetry paths, where spin-up and spin-down bands are represented by red and blue dashed lines, respectively. (d) Band structures at symmetry-equivalent paths within the BZ, highlighting the inversion of spin-up and spin-down bands due to symmetry operations. (e) Two-dimensional contour plot of spin splitting ($\Delta E$) at $k_z = 0.5$, showing the plane with maximal spin splitting. (f) The Fermi surface cut at $k_z$$=$ 0, through the $\Gamma$$-$X$-$M plane, illustrating spin-up (red) and spin-down (blue) contributions. (g--h) Three-dimensional (3D) spin-resolved Fermi surfaces for (g) spin-up and (h) spin-down electronic states, emphasizing spin-dependent characteristics. Note that the absolute orientation of the collinear spin axis does not affect DFT calculations without spin-orbit coupling, hence, in our pictures the spin directions are shown as computed (in +/- z direction) rather than as reported for the respective structures.
• Figure 3: Structural, electronic, and spin-resolved properties of NbMnP. (a) Side view of the crystal structure of NbMnP, illustrating the AFM configuration with spins aligned along the z-axis on the Mn sites. (b) Corresponding BZ indicating key high-symmetry points. (c) Spin-polarized electronic band structure along standard high-symmetry paths, with spin-up and spin-down channels represented by red and blue lines, respectively. (d) Spin-resolved band structure along the $\Delta_{max}-\Gamma-\Delta_{max}^{\prime}$ path, highlighting the symmetry-enforced spin reversal. (e) 2D contour map of the spin-splitting magnitude ($\Delta E$) on the $k_z = 0.25$ plane. (f) Spin-resolved Fermi surface cut at $k_z$=0.25 plane. These contours are anisotropic and exhibit a $180^\circ$ rotation between the spin channels. (g) and (h) 3D spin-resolved Fermi surfaces for the spin-up and spin-down channels, respectively, showing complementary shapes related by $k_x \leftrightarrow -k_x$ and a spin flip.
• Figure 4: Structural, electronic, and spin-resolved properties of YRuO$_3$. (a) Unit cell of YRuO$_3$, illustrating the atomic arrangement and the AFM spin configuration. Large light green spheres represent Y atoms, small red spheres represent O atoms, and yellow spheres represent Ru atoms. (b) Bulk Brillouin zone of YRuO$_3$ with high-symmetry points labeled. (c) Spin-polarized electronic band structure of YRuO$_3$ along high-symmetry directions. Red solid lines indicate spin-up bands, and blue dashed lines represent spin-down bands. (d) Detailed view of the spin-polarized band structure along two symmetry-equivalent paths within the BZ, highlighting the spin inversion features. (e) 2D contour plot of the spin splitting $\Delta$E in the k$_z$=0.4 plane, identifying regions of maximal spin-momentum locking. (f) Spin texture visualized in the 001 plane, showing the orientation and magnitude of the spin polarization for selected states.